2010/11/18 by Robert D. Gray, Robert Gray, Gray, Robert +7
Computer Science · Mathematics · #05C20 #05C25 #05C75 #20B05 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Limits and Structures in Graph Theory #math.CO #math.GR #msc:05C20 #msc:05C25 #msc:05C75 #msc:20B05
paper · pdf · doi:10.48550/arxiv.1011.4216
43 pages
arxiv created 2010/11/18 · openalex publication_date 2010/11/18 · arxiv updated 2010/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A directed graph is set-homogeneous if, whenever U and V are isomorphic finite subdigraphs, there is an automorphism g of the digraph with Ug=V. Here, extending work of Lachlan on finite homogeneous digraphs, we classify finite set-homogeneous digraphs, where we allow some pairs of vertices to have arcs in both directions. Under the assumption that such pairs of vertices are not allowed, we obtain initial results on countably infinite set-homogeneous digraphs, classifying those which are not 2-homogeneous.